Fuselage shaping to reduce the strength of shock waves about airplanes at transonic and supersonic speeds



959 R. T. WHlTCOM 2,874,922-

FUSELAGE SHAPING 1'0 REDUCE THE STRENGTH OF SHOCK WAVES ABOUT AIRPLANES AT TRANSONIC AND SUPERSONIC SPEEDS Filed Aug. 24, 1956 5 Sheets-Sheet 1 FIG.

INVENTOR 'fli. RICHARD r wn/raoma ATTORNEYS Feb. 24, 1959 R. T. WHITCOMB 2,874,922 FUSELAGE SHAPING 1'0 REDUCE THE STRENGTH OF SHOCK WAVES ABOUT AIRPLANES AT TRANSONIC AND SUPERSONIC SPEEDS Filed Aug. 24, 1956 5 Sheets-Sheet 2 I N VEN TOR RICHARD I WH/ 700MB ATTORNEYS FUSELAGE SHAPING :[O REDUCE THE STRENGTH OF SHOCK WAVES ABOUT AIRPLANES AT TRANSONIC' AND SUPERSONIC SPEEDS 1959 R WHITCOMB 2,874,922

Fil ed Aug. 24, 1956 3 Sheets-Sheet 3 RIG/MRO 7. WI 760MB ATTORNEYS FUSELAGE SHAPING TO REDUCE THE STRENGTH F SHOCK WAVES ABOUT AIRPLANES AT TRANSONIC AND SUPER- SONIC SPEEDS Richard T. Whitcomb, Hampton, Va. Application August 24, 1956, Serial No. 6 116,176

Claims. Cl. 244-430 (Granted under Title 35, U. S. Code (1952), sec. 266) The invention described hereinmay be manufactured and used by or for the Government of the United States of America for governmental purposes without the payment of any royalties thereon or therefor.

When the speed of an airplane approaches and exceeds the speed of sound, shock waves form about the configuration. These shock waves cause a marked increase in drag, or air resistance, buffet, noise, stability problems, and other adverse aerodynamic effects. It is an object of the present invention to reduce the strength of these shock Waves and thus reduce the wave drag and other adverse effects through the proper shaping of the fuselage.

, Ithas been found that the form and strength of the shock waves are dependent not on the forms of the individual components such as the wing, fuselage, and tail but on the form of the entire configuration as a whole. Further, it has been found that the form and strength of the shock waves near the speed of sound are primarily dependent on the longitudinal or streamwise development of the cross-sectional areas of the conguration normal to the airstream. Also, it has been found that at moderate supersonic speeds, the form and strength of the shock waves are primarily dependent on the longitudinal development of normal components of cross-sectional areas obtained with planes through the configuration which are inclined to the direction of the airstream. Since the shock strength at transonic and moderate supersonic speeds is primarily dependent on the longitudinal developments of cross-sectional area for the complete configuration, it is proposed that to reduce the shock strength for airplanes at these speeds, the volume of the fuselage or other components be distributed longitudinally such that this development of area for the complete configuration be such as theory and experiment indicate will produce weaker shock waves. With such a distribution of volume, the fuselage will usually have reversals of curvature in the longitudinal regions of the wing, tail surfaces, canopy, nacelles, etc.

, The shapings produced with the present invention are arrived at by considering the flow over the complete eonfiguration. Experiments indicate that the shapings provided by the present invention are effective in reducing the strength of shock waves for airplane configurations with all types of wings, and is not limited to airplane configurations with swept wings.

Reference is now made to the following description taken in connection with the accompanyingdrawings in which:

Fig. 1 is a diagram illustrating the procedure for ar-. riving at the longitudinal development of fuselage crosssectional area for reduced shock strength.

Fig. 2a is a plan view of a typical unswept wing-airplane configuration with the fuselage volume distributed on the basis of the present invention.

Fig. 2b is a plan view of a typical unswept wingair plane configuration with the fuselage volume distributed normally.

Fig. 3

is a diagram comparing the longitudinal de 1 velopments of cross-sectional area for the configurations of Fig. 2a and Fig. 2b.

Fig. 4 is a diagram illustrating the procedure for arriving at the fuselage area development when certain cross-sectional areas of the fuselage are fixed.

Fig. 5 is a diagram illustrating the procedure for determining areas to be added to the fuselage of an existing airplane design to obtain reductions in shock strength.

Fig. 6a shows a typical airplane configuration.

Fig. 6b shows the airplane configuration of Fig. 6a

with volume added to obtain reductionsin shock strengthJ Fig. 7a illustrates the procedures for obtaining crosssectional areas of the wing used to obtain fuselage shaping which provides reduction in shock strength at a supersonic speed.

Fig. 7b is the longitudinal development of cross-sectional areas corresponding to Fig. 7a.

Fig. 8a illustrates the procedure for obtaining crosssectional. areas of the wing used to obtain fuselage shaping which provides reduction in shock strength at another supersonic speed.

, Fig. 8b is the longitudinal development of cross-sectional areas corresponding to Fig. 8a.

Referring now to the drawings, there is shown in Fig.' l a horizontal line which represents the length of a particular aircraft. The curve 10 is the longitudinal development of cross-sectional area for an airplane that equals or approaches the development which theory or experiment indicates provides minimum shock strength at transonic or moderate supersonic speeds. In this case the Fig. 1 diagram is for the special conditions of fixed airplane length and volume. The areas 11, 12 and 13 are the normal cross-sectional areas of the pilot canopy, wing and tail surfaces, respectively. These areas are subtracted from the total cross-sectionaldevelopment, represented by curve 10, to arrive at a fuselage area represented by the dotted line 14. The areas for other external parts such as nacelles would be subtracted in a similar manner. With such a development of the cross-sectional area for the fuselage, the fuselage of the configuration may appear as shown in Fig. 2a with reversal in curvature of the lines near the canopy 15, the wing 16 and the tail 17. For comparison, a normal streamlined fuselage with the same volume as that of Fig. 2a is shown in Fig. 2b. The longitudinal development of total crosssectional area for the airplane with the specially shaped fuselage shown in Fig. 2a is compared with that for the airplane with the streamlined fuselage shown in Fig. 2b

in Fig. 3. In this figure the solid line 18 is the area development for the configuration with the specially shaped fuselage (Fig. 2a) and may be seen to be free of severe maximum slopes or changes in slope, whereas the dotted line 19 represents the longitudinal development of crosssectional area for the configuration with the streamlined fuselage (Fig. 2b) and may be seen to have relatively severe slopes of area relative to length, as at 20, and abrupt changes of these slopes, as at 21. The severe slopes of area with length and abrupt changes of these slopes produce relatively strong shock waves. On the other hand, near the speed of sound, the aircraft represented by the curve 18 and Fig. 2a has shock waves which are much weaker than that with the streamlined fuselage and the wave drag and other adverse effects associated with the shock waves are much less.

For most airplane designs, certain total cross-sectional areas cannot be reduced beyond certain minimums because of the presence of fixed equipment inside the fuselage such as engines, landing gears, electronic equipment, etc. InFig. 4 there is shown the beginning of the longitudinal development of cross-sectional area for anairplane, in which curve 25 represents the fixed minimum area for the fuselage plus canopy, curve 26 represents the fixed minimum for'the fuselage plus wing and curve 27 represents the fixed minimum area for the fuselage nliis. a. urfa e Wi h th s imi ations h iis r h ir. tion of "fuselagevolur'neis determined. bysubtracting the no mal rosssec ie al area for h ca opy; wing; a d t surfaces r m he long udin l development of the tot l cross-s'ecti' area, that equals of approaches the del p rie it'whi hpr v des minimum shock stren th wh nclo i gthe .fixedjar a, li h'a dev lopmen ngr p esented. y he. dotted; line; curv 28 o H s The present invention may also be used to reduce the shock ngth f. xi t ng. ai p a e des ns hrou dition s of volume tot fuselage. In Fig.5 the solid line 30.x. re entsthe. ongit, nal deve op seetier l area. fo h 'typ" a1,represe ta iv s. x s i i plane. sh wn. n. g; 6a; his l ng t dinal. de opmen of o a .cros rse tinnal area may h hanged by a li g. volume to'the airplane fuselage so that 't e modifled an n anehas a. on itudinal,dey orrnent' t al cross sectional area as represented by the-dashed line 31 Since he. maximum. lopes. f ar j i h'l ig h nd h rup changeslof slope are considerablyl ess, 'the shock strength or h m dified on gur tion is on der ly m ll r h n that for the existing configuration. figu ation. is.., ho.wn. in. .E b-

The longitudinal distribution of total cross scctional area for the total airplane need not necessarily be exactly ha or m imum sho' k trength to t in. n fica t r ductions in shock strength. It need only approach the m nim shock.developm nt.v o ample or th airplane"co-nfigurationofFig, 6g, represented by curve F ghe diti n of urne of he u e e ahea 'and behind. he ihgte e h lo udina development o-f total cross-sectional area represented. by the dotted curve 32 of Fig. 5 would provide a reduction in shock'stre gth nearly as great as that obtained with he. p um adit d pro ide. t eve opment. f t ta rea. w thmi mi m ho reng as rep e e y ur 111 F g, 5-.

3 ome nfisuratienst e a i ma n t de f h cr ss-s ti n are f r. the canopy. wing r a su aees. ay b ch. ha wh n. he, area o he e co pane t are subtr ct d romthe e e opm nt. of to a o 0 1. are s. or m im m sho k s r n t h r su longitudinal development of the cross-sectional area for he fuse e IHQY IOI inc rp a reversal o the curvaturesuch as. is shown in Figs. 2a and 6'1), but may have ely regio of. ela v y grad a hang f s op i th vi inity of the e components. Nevertheless, the use o. h.e pecial-dist ibu ion o f se m o pr i this pa. .ei lon i dinal d e pmen otal r a will result in reduced shock strength for the configuration.

The ab di cussi n i v ap a to p ed at r nea e oni sp ed whe in h r an e p oduc n hock, wav s. are su stan ly orma to h r stream- A m e te supe soni speeds, h is rb nces p od ced y a onfi'g rat on a ia e' a tigeo es, the ele of whichjare inclined to the air stream'at the Mach angle. Parenthetically, it may be noted that the sine of the Mach angle is equal to the speedofsound divided by the forward; oeityo o ta n. e. o d n str u ion ofthe, volume for the fuselage which provides reduced shock strength at moderate supersonic speeds, the proce ure escr bed bo e s. d fied y a mo e d t analysis of the wing and tail surfaces cross-sectional areas, and'of otherfezrternal components such as stores, etc.

Ie btaina comple e t ade el pmen or a in in hei persen" 'a eta utting. Pl ne, eat to a i etheh ,eone with th eoneaxis at or The modified coniea the a. at. he Me h.

win a a. s ccess on. eff longi ud a stat ons. InE s- 761;. this i .ill stratedby th u t ng-plan 36 angen o a it ffl eta eros Mach cone 40 along the element 41 thereof and passed through the wing 35' at a Mach angle 38', arrow 37"desig-- nating the air stream direction. The area obtained at each pass of the intercepted cross-sectional plane 36 is projected normal to the air stream, The area development shown at 39 in Fig. 7b illustrates: a development'obtained y he s e essive'pa s e n nelfi ht ush in95,

Thereafter, the cuttingplaneis,rotatedgto be, ngent t heMaeheoneAfl a onaanether eleme t he eotft r h a o e o e l t i r a d-fe etail writ rs-r The arithmetical average ofj thewing area 'or taildevelopments 'o'btained' with the various "rotations of the cutting plane iss'ubtracted' from a development of total area in a'manner similar to that utilized with one area de; velopmentfo'r the wing or tailffor a design for near the speed-of sound. Area developments obtained for the, wing or tail with the cutting' plane rotated to several positions provides indications of the longitudinaldistribu tions of the fuselage volume of minimum shock streng t h' for most airplanes.

At sonic speeds and above, the disturbances produced' by the airplane which produce adverse shock waves radi ate in all directions. Those directed toward the wingo'r tailsurfaces are refiectedback, in muchthe same manner; as a mirror reflects light waves. As a result, disturb} ances produced on one side of such a wing; surfaceihas little influence on the shock waves on the otherside of the surface. To most satisfactorily define these shocleproducing disturbances, the crossrse-ctionalj areas obtained by'the cutting planes are divided at the wing plane.

areas for directly above and below'the wing and hories tail. ane a ep o d l tud na ly an 9s: e e sep ai ly- O us y ma y mod fi ations nd v r a io of. h pr en invention re Pos n he h o h be teachings. It is therefore to beunders tood' thatiwithin h en Q h ppend cla m h h eiit 'e' i a e.

c iced o er is ha as sp i a y, scri ed,

What is claimed is:

2 h a pla n h eht e essec io al. ealiri. p ane ene l y perpend e l r. t0 he lon tudina axi a n y a ub ant a ly decreas n e. j gefrlzin.

near the nose aft until the rate of change 1s z ero,]a nd as rearwa d y of the zer at o hange. P i t Q ilya sub an ia y n a ive y increa in r te. h ge- An airplane. i w eh heia o o nq ees njthe. cro sr e iena r pe i l th. n P anes, ge era y pe n e lar to the lo. l i i. v axis. is. hs't ll constant from near'the nose to near the maximumtoss: sectional area.

3. In an airplane having a protruding cockpit canopy, a fuselage indented. from normal configuration in the vicinity of said canopy, wherebythe totalcross-Isectional area of said aircraft in the vicinity Of, said canopy is only gradually increased,

4. In an airplane, a fuselage, a protuberance extending from said fuselage, said fuselage being indented in the vicinity of said protuberance, the volume of said indentation from normal streamline configuration being; approximately equal to the volume of said' protuberance.

5; In an airplane, a fuselage, a protuberance extendingt m a se a e. d. u el ge ing. i ei ed n the vie/ihity Qt, i.-.Pi9 uhe.rme th o a of; h la n: tation from normal streamline configuration at a the fuselage longitudinal axis, being approximately equal to the total area of said protuberance in said plane.

6. An airplane having a fuselage in which the total cross-sectional area, comprising a first cross-sectional area taken of the fuselage in a plane generally perpendicular to the longitudinal axis and a second cross-sectional area taken of components external to the fuselage in planes tangent to the Mach cone whose axis is substantially on the central longitudinal axis of the airplane and projected normally to the airstream, gradually increases to a maximum and then decreases from nose to tail.

7. An airplane having a fuselage in which the total cross-sectional area, comprising a first cross-sectional area taken of the fuselage in a plane generally perpendicular to the longitudinal axis and a second cross-sectional area taken of components external to the fuselage in planes tangent to the Mach cone whose axis is substantially on the central longitudinal axis of the airplane and projected normally to the airstream has a decreasing rate of change from near the nose aft until the rate of change is zero, and has rearwardly of the zero rate of change point a negatively increasing rate of change.

8. An airplane having a fuselage in which there are only small changes in the total cross-sectional area thereof from nose to tail, said total cross-sectional area comprising a first cross-sectional area taken of the fuselage in a plane generally perpendicular to the longitudinal axis and a second cross-sectional area taken of components external to the fuselage in planes tangent to the Mach cone whose axis is substantially on the central longitudinal axis of the airplane and projected normally to the airstream.

9. An airplane having a fuselage in which the rate of increase in the total cross-sectional area per unit length is substantially constant from near the nose to near the maximum cross-sectional area, said total cross-sectional area comprising a first cross-sectional area taken of the fuselage in a plane generally perpendicular to the longitudinal axis and a second cross-sectiona1 area taken of components external to the fuselage in planes tangent to the Mach cone whose axis is substantially on the central longitudinal axis of the airplane and projected normally to the airstream.

10. An airplane having a fuselage in which there are only small changes in the rate of increase in the total cross-sectional area per unit length, said total cross-sectional area comprising a first cross-sectional area taken of the fuselage in a plane generally perpendicular to the longitudinal axis and a second cross-sectional area taken of components external to the fuselage in planes tangent to the Mach cone whose axis is substantially on the cen tral longitudinal axis of the airplane and projected normally to the airstream.

References Cited in the file of this patent FOREIGN PATENTS 301,390 Germany June 28, 1920 459,307 Italy Sept. 5, 1950 477,206 France -l July 6, 1915 931,003 France Sept. 15, 1947 932,410 Germany Sept. 1, 1955 

